The elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ and its vertex operators

Details The elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ and its vertex operators The elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ and its vertex operators

2008-12-05

arxiv.org/abs/0812.1147v2

J.Phys.A42:425202,2009

Mathematics

Quantum Algebra

28 pages

Scientific paper

10.1088/1751-8113/42/42/425202

We construct a realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for any given level $k$ in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization of the quantum affine algebra $U_{q}(\hat{sl_N})$. We also construct a family of screening currents, which commute with the currents of $U_{q,p}(\hat{sl_N})$ up to total q-differences. And we give explicit twisted expressions for the type $I$ and the type $II$ vertex operators of $U_{q,p}(\hat{sl_N})$ by twisting the known results of the type $I$ vertex operators of the quantum affine algebra $U_{q}(\hat{sl_N})$ and the new results of the type $II$ vertex operators of $U_{q}(\hat{sl_N})$ we obtained in this paper.

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